声电层析成像的可行性
Feasibility of Acousto-Electric Tomography
AI总结：
该研究针对声电层析成像的电导率重建问题，提出两步式反演框架，通过数值实验验证了该方法在不同参数与噪声条件下的可行性，并证实有限角度场景下边界附近重建效果良好。
摘要：
声电层析成像的目标是，在时域声波穿透待测区域的条件下，通过对应电流与电压的静电边界测量结果，重建区域内的电导率。我们对该现象建立了显式模型，并提出一套完整的声电层析成像反演框架，分为两个步骤：第一步，通过求解一个线性不适定问题，从边界测量结果中得到内部功率密度；第二步，通过求解一个非线性、适定性较好的问题，由功率密度重建内部电导率。我们采用参数符合实际情况的合成数据开展数值实验，探究了从边界测量结果重建电导率的可行性如何受声电耦合常数与测量噪声的影响。研究结果呈正向，表明AET（声电层析成像）在医学成像等相关应用中确实具备可行性。最后，我们研究了有限角度场景，证明在测量边界附近区域可实现良好的电导率重建。
英文摘要：
In acousto-electric tomography the goal is to reconstruct the electric conductivity in a domain from electrostatic boundary measurements of corresponding currents and voltages, while the domain is penetrated by a time-dependent acoustic wave. We explicitly model the phenomena, and we propose a complete inversion framework for acousto-electric tomography in two steps: First the interior power density is obtained from boundary measurements by solving a linear, ill-posed problem; second the interior conductivity is reconstructed from the power density by solving a non-linear, fairly well-posed problem. We perform numerical experiments on synthetic data with realistically chosen parameters. We investigate how feasibility of reconstructing the electrical conductivity from boundary measurements depends on the acousto-electric coupling constant and measurement noise. Our findings are positive, and indicate that AET is indeed feasible for interesting applications in for example medical imaging. Finally, we consider a limited angle setup and show that the conductivity is well reconstructed near the measurement boundary.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
